$x≔5$

$x:=5$

$\mathrm{fsolve}\left(23 x^5\+103 x^4 -10 x\,x\right)$

Error, (in fsolve) invalid arguments

$x≔\'x\'\;$

$x:=x$

$\mathrm{fsolve}\left(23 x^5\+103 x^4 -10 x\,x\right)$

$-4.483086353\,0.\,0.4453115351$

$g ≔ .2189750324\;$

$g:=0.2189750324$

$m ≔ 1\;$

$m:=1$

$a ≔ 1\;$

$a:=1$

$c ≔ 2\;$

$c:=2$

$\mathrm{equation1} ≔ y \= m\cdot X\+c\;$

$\mathrm{equation1}:=y\=X\+2$

$\mathrm{area1} ≔ \mathrm{int}\left(\mathrm{equation1}\, X \= g .. a\, \mathrm{numeric}\right)\;$

Error, (in int) invalid arguments

$\mathrm{type}\left(\mathrm{equation1}\,\mathrm{algebraic}\right)$

$\mathrm{false}$

$\mathrm{restart}$

$g ≔ .2189750324\;$

$g:=0.2189750324$

$m≔ 1\;$

$m:=1$

$a ≔ 1\;$

$a:=1$

$c≔ 2\;$

$c:=2$

$\mathrm{expression} ≔ m\cdot X\+c\;$

$\mathrm{expression}:=X\+2$

$\mathrm{area1} ≔ \mathrm{int}\left(\mathrm{expression}\, X \= g .. a\, \mathrm{numeric}\right)\;$

$\mathrm{area1}:=2.038074903$

$\mathrm{type}\left(\mathrm{expression}\,\mathrm{algebraic}\right)$

$\mathrm{true}$

$\mathrm{restart}\;$

$\mathrm{sys} ≔ \left\{\mathrm{diff}\left(\mathrm{f1}\left(x\right)\, x\, x\right)-\mathrm{f1}\left(x\right)\+\mathrm{f2}\left(x\right) \= 0\, \mathrm{diff}\left(\mathrm{f2}\left(x\right)\, x\, x\right)-\mathrm{f2}\left(x\right)\+\mathrm{f3}\left(x\right)\+\left(\mathrm{f1}\left(x\right)-\mathrm{f2}\left(x\right)\right) \= 0\, \mathrm{diff}\left(\mathrm{f4}\left(x\right)\, x\, x\right)\+\left(\mathrm{f3}\left(x\right)-\mathrm{f4}\left(x\right)\right) \= 0\, \mathrm{diff}\left(\mathrm{f3}\left(x\right)\, x\, x\right)-\mathrm{f3}\left(x\right)\+\mathrm{f4}\left(x\right)\+\left(\mathrm{f2}\left(x\right)-\mathrm{f3}\left(x\right)\right) \= 0\right\}\;$

$\mathrm{sys}:=\left\{\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f1}\left(x\right)-\mathrm{f1}\left(x\right)\+\mathrm{f2}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f4}\left(x\right)\+\mathrm{f3}\left(x\right)-\mathrm{f4}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f2}\left(x\right)-2\mathrm{f2}\left(x\right)\+\mathrm{f3}\left(x\right)\+\mathrm{f1}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f3}\left(x\right)-2\mathrm{f3}\left(x\right)\+\mathrm{f4}\left(x\right)\+\mathrm{f2}\left(x\right)\=0\right\}$

$\mathrm{ics} ≔ \mathrm{f1}\left(0\right) \= 0\, \mathrm{f2}\left(0\right) \= 0\, \mathrm{f3}\left(0\right) \= 0\, \mathrm{f4}\left(0\right) \= r$

$\mathrm{ics}:=\mathrm{f1}\left(0\right)\=0\,\mathrm{f2}\left(0\right)\=0\,\mathrm{f3}\left(0\right)\=0\,\mathrm{f4}\left(0\right)\=r$

$\mathrm{sol} ≔ \mathrm{dsolve}\left(\left\{\mathrm{sys}\, \mathrm{ics}\right\}\right)$

Error, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received: {{diff(diff(f1(x), x), x)-f1(x)+f2(x) = 0, diff(diff(f4(x), x), x)+f3(x)-f4(x) = 0, diff(diff(f2(x), x), x)-2*f2(x)+f3(x)+f1(x) = 0, diff(diff(f3(x), x), x)-2*f3(x)+f4(x)+f2(x) = 0}}

$\mathrm{type}\left(\left\{\mathrm{sys}\,\mathrm{ics}\right\}\,\left\{\mathrm{set}\right\}\left(\mathrm{equation}\right)\right)$

$\mathrm{false}$

$\mathrm{sys} ≔ \mathrm{diff}\left(\mathrm{f1}\left(x\right)\, x\, x\right)-\mathrm{f1}\left(x\right)\+\mathrm{f2}\left(x\right) \= 0\, \mathrm{diff}\left(\mathrm{f2}\left(x\right)\, x\, x\right)-\mathrm{f2}\left(x\right)\+\mathrm{f3}\left(x\right)\+\left(\mathrm{f1}\left(x\right)-\mathrm{f2}\left(x\right)\right) \= 0\, \mathrm{diff}\left(\mathrm{f4}\left(x\right)\, x\, x\right)\+\left(\mathrm{f3}\left(x\right)-\mathrm{f4}\left(x\right)\right) \= 0\, \mathrm{diff}\left(\mathrm{f3}\left(x\right)\, x\, x\right)-\mathrm{f3}\left(x\right)\+\mathrm{f4}\left(x\right)\+\left(\mathrm{f2}\left(x\right)-\mathrm{f3}\left(x\right)\right) \= 0\;$

$\mathrm{sys}:=\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f1}\left(x\right)-\mathrm{f1}\left(x\right)\+\mathrm{f2}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f2}\left(x\right)-2\mathrm{f2}\left(x\right)\+\mathrm{f3}\left(x\right)\+\mathrm{f1}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f4}\left(x\right)\+\mathrm{f3}\left(x\right)-\mathrm{f4}\left(x\right)\=0\,\frac{{\ⅆ}^2}{\ⅆx^2}\mathrm{f3}\left(x\right)-2\mathrm{f3}\left(x\right)\+\mathrm{f4}\left(x\right)\+\mathrm{f2}\left(x\right)\=0$

$\mathrm{ics} ≔ \mathrm{f1}\left(0\right) \= 0\, \mathrm{f2}\left(0\right) \= 0\, \mathrm{f3}\left(0\right) \= 0\, \mathrm{f4}\left(0\right) \= r$

$\mathrm{ics}:=\mathrm{f1}\left(0\right)\=0\,\mathrm{f2}\left(0\right)\=0\,\mathrm{f3}\left(0\right)\=0\,\mathrm{f4}\left(0\right)\=r$

$\mathrm{sol} ≔ \mathrm{dsolve}\left(\left\{\mathrm{sys}\, \mathrm{ics}\right\}\right)$

$\mathrm{sol}:=\left\{\mathrm{f1}\left(x\right)\=\frac{1}{4}r\+\mathrm{\_C2}x\+\left(-\mathrm{\_C4}\+\frac{1}{4}r\right){\ⅇ}^{\sqrt{2}x}\+\mathrm{\_C4}{\ⅇ}^{-\sqrt{2}x}\+\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}\+\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}-\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}\+\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\,\mathrm{f2}\left(x\right)\=-\left(-\mathrm{\_C4}\+\frac{1}{4}r\right){\ⅇ}^{\sqrt{2}x}-\mathrm{\_C4}{\ⅇ}^{-\sqrt{2}x}-\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}-\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}\sqrt{2}-\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}-\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}\sqrt{2}\+\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}-\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}\sqrt{2}-\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\+\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\sqrt{2}\+\frac{1}{4}r\+\mathrm{\_C2}x\,\mathrm{f3}\left(x\right)\=\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}\+\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}-\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}\+\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\+\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}\sqrt{2}\+\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}\sqrt{2}\+\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}\sqrt{2}-\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\sqrt{2}-\left(-\mathrm{\_C4}\+\frac{1}{4}r\right){\ⅇ}^{\sqrt{2}x}-\mathrm{\_C4}{\ⅇ}^{-\sqrt{2}x}\+\frac{1}{4}r\+\mathrm{\_C2}x\,\mathrm{f4}\left(x\right)\=-\left(-\mathrm{\_C6}-\frac{1}{4}r\+\frac{1}{8}\sqrt{2}r\right){\ⅇ}^{-\sqrt{2\+\sqrt{2}}x}-\mathrm{\_C6}{\ⅇ}^{\sqrt{2\+\sqrt{2}}x}\+\frac{1}{8}\left(2\+\sqrt{2}\right)\left(8\mathrm{\_C8}\+r-4\mathrm{\_C8}\sqrt{2}\right){\ⅇ}^{-\sqrt{2-\sqrt{2}}x}-\mathrm{\_C8}{\ⅇ}^{\sqrt{2-\sqrt{2}}x}\+\left(-\mathrm{\_C4}\+\frac{1}{4}r\right){\ⅇ}^{\sqrt{2}x}\+\mathrm{\_C4}{\ⅇ}^{-\sqrt{2}x}\+\frac{1}{4}r\+\mathrm{\_C2}x\right\}$